Problem: Simplify the following expression: $ r = -2 - \dfrac{5k}{5k + 3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5k + 3}{5k + 3}$ $ \dfrac{-2}{1} \times \dfrac{5k + 3}{5k + 3} = \dfrac{-10k - 6}{5k + 3} $ Therefore $ r = \dfrac{-10k - 6}{5k + 3} - \dfrac{5k}{5k + 3} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-10k - 6 - 5k }{5k + 3} $ Distribute the negative sign: $r = \dfrac{-10k - 6 - 5k}{5k + 3}$ $r = \dfrac{-15k - 6}{5k + 3}$